Is a Black Hole's Entropy Truly Lost?

[Quds Akbar]

I know that a black hole sucks stuff into a singularity, and I know about the second law of thermodynamics (that the entropy in an isolated system can only stay the same or increase), so if a black hole sucks something in it reduces the total entropy of the Universe, right? This was brought up in one of the books I have read but I could not comprehend whether or not the second law is broken or not and if it is not then how that entropy is "conserved", so could anybody please explain?

 

[Rmehtany]

Dear Quds Akbar,

This question has befuddled many in the past, and is a bit hard to get one's mind around. The truth is that a black hole 'eats up' entropy whenever its sucks in matter (as you've noticed,) so it has to compensate in some way. This proves that first, black holes have entropy, and second, they must 'return' some of that entropy. That's why black holes emit high energy waves which compensate for the absorbed entropy. There is a formula called the Bekenstein-Hawking formula for calculating this entropy and much more. If you are interested, follow the link: http://en.wikipedia.org/wiki/Black_hole_thermodynamics#The_laws_of_black_hole_mechanics

 

[wabbit]

I don't know if I should start a different thread about this, but there is something I find unsatisactory in this answer because it relies on QFT to explain the entropy - but what about a strictly classical black hole in non-QM spacetime ? The question is still well posed here, and the idea that a singularity is just outside the theory only goes that far : after all it seems to me that singularity can be viiewed as nothing more than a point mass, and this is not usually a deal-breaker. How would one address the question in this setup ?

Of course the horizon remains, and there is the issue of what entropy relative to what observer we are talking about, so maybe the question isn't posed explicitly enough too.

 

[Rmehtany]

Here are different ways of resolving the issue:

Information is irretrievably lost

• Advantage: Seems to be a direct consequence of relatively non-controversial calculation based on semicalssical gravity.
• Disadvantage: Violates unitarity, as well as energy conservation or causality.

Information gradually leaks out during the black-hole evaporation

• Advantage: Intuitively appealing because it qualitatively resembles information recovery in a classical process of burning.
• Disadvantage: Requires a large deviation from classical and semiclassical gravity (which do not allow information to leak out from the black hole) even for macroscopic black holes for which classical and semiclassical approximations are expected to be good approximations.

Information suddenly escapes out during the final stage of black-hole evaporation

• Advantage: A significant deviation from classical and semiclassical gravity is needed only in the regime in which the effects of quantum gravity are expected to dominate.
• Disadvantage: Just before the sudden escape of information, a very small black hole must be able to store an arbitrary amount of information, which violates the Bekenstein Bound.

Information is stored in a Planck-sized remnant

• Advantage: No mechanism for information escape is needed.
• Disadvantage: To contain the information from any evaporated black hole, the remnants would need to have an infinite number of internal states. It has been argued that it would be possible to produce an infinite amount of pairs of these remnants since they are small and indistinguishable from the perspective of the low-energy effective theory.

Information is stored in a baby universe that separates from our own universe.

• Advantage: This scenario is predicted by the Einstein-Cartan of gravity which extends general relativity to matter with intrinsic angular momentum. No violation of known general principles of physics is needed.
• Disadvantage: It is difficult to test the Einstein–Cartan theory because its predictions are significantly different from general-relativistic ones only at extremely high densities.

Information is encoded in the correlations between future and past

• Advantage: Semiclassical gravity is sufficient, i.e., the solution does not depend on details of (still not well understood) quantum gravity.
• Disadvantage: Contradicts the intuitive view of nature as an entity that evolves with time.

In other words, there is no appealing solution to the question without quantum mechanics

 

[wabbit]

Actually, I am having trouble even before that... remaining in a strictly classical setup, which information is lost ? For a distant hovering or orbiting observer, nothing ever crosses the horizon and all is fine it seems. So presumably the issue arises for a free falling observer - but then I am very confused as to what he sees as I find it difficult to reconcile the usual "nothing special happens as he crosses the horizon" with the fact that he must be unable to see his feet anymore if they are first to cross the horizon.

 

[Quds Akbar]

Is there any possibility for this have to do anything with Dark Matter?

 

[Rmehtany]

This is beyond my knowledge. I'll do my research.

 

[Quds Akbar]

This proves that first, black holes have entropy, and second, they must 'return' some of that entropy. That's why black holes emit high energy waves which compensate for the absorbed entropy.

But how do these energy waves escape the event horizon? It would break relativity. And if they were particles from the outside then would they would not count as "returning that entropy" because they are part of the outside entropy, so how would it emit particles?

 

[wabbit]

But how do these energy waves escape the event horizon? It would break relativity.

Hawking radiation is a (semi-classical) quantum effect, absent in classical GR. It can be tought of as particles (photons or other) tunnelling through the horizon.

For most of the life of a black hole, this is a very tiny effect - but if the black hole isn't fed enough incoming matter and radiation to compensate for this very slow evaporation, it loses mass and shrinks accordingly. This starts very slowly, but given enough time (many billions of years for a stellar mass black hole), this is a runaway process (the smaller the black hole, the more it radiates) that, in the standard picture, ends in a flash resulting in the black hole (and horizon) disappearance.

As far as I can tell, whether and how this process returns all or part of the "lost entropy" to the outside universe is a much debated question which is not fully settled. Also, it is not clear that this process accounts for the whole story as it is built on a semi-classical account which may fail in the late stages of the evaporation, as this may require a full quantum gravity treatment.

Lastly, Hawking radiation is a theoretical prediction, it has not to the best of my knowledge ever been observationally described (the closest to that might be in black hole analogues, not involving gravity) - so even if the prediction looks solid, conclusions about it are also theoretical predictions, not established fact.

 

[Quds Akbar]

Here are different ways of resolving the issue:

Information is irretrievably lost

• Advantage: Seems to be a direct consequence of relatively non-controversial calculation based on semicalssical gravity.
• Disadvantage: Violates unitarity, as well as energy conservation or causality.

Information gradually leaks out during the black-hole evaporation

• Advantage: Intuitively appealing because it qualitatively resembles information recovery in a classical process of burning.
• Disadvantage: Requires a large deviation from classical and semiclassical gravity (which do not allow information to leak out from the black hole) even for macroscopic black holes for which classical and semiclassical approximations are expected to be good approximations.

Information suddenly escapes out during the final stage of black-hole evaporation

• Advantage: A significant deviation from classical and semiclassical gravity is needed only in the regime in which the effects of quantum gravity are expected to dominate.
• Disadvantage: Just before the sudden escape of information, a very small black hole must be able to store an arbitrary amount of information, which violates the Bekenstein Bound.

Information is stored in a Planck-sized remnant

• Advantage: No mechanism for information escape is needed.
• Disadvantage: To contain the information from any evaporated black hole, the remnants would need to have an infinite number of internal states. It has been argued that it would be possible to produce an infinite amount of pairs of these remnants since they are small and indistinguishable from the perspective of the low-energy effective theory.

Information is stored in a baby universe that separates from our own universe.

• Advantage: This scenario is predicted by the Einstein-Cartan of gravity which extends general relativity to matter with intrinsic angular momentum. No violation of known general principles of physics is needed.
• Disadvantage: It is difficult to test the Einstein–Cartan theory because its predictions are significantly different from general-relativistic ones only at extremely high densities.

Information is encoded in the correlations between future and past

• Advantage: Semiclassical gravity is sufficient, i.e., the solution does not depend on details of (still not well understood) quantum gravity.
• Disadvantage: Contradicts the intuitive view of nature as an entity that evolves with time.

In other words, there is no appealing solution to the question without quantum mechanics

I am writing about something similar to this lately, and I was just wondering if it was okay for you to provide the source/citations for this information if you can.
And thanks in advance.